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The data are collected in time-snapshots denoted by ηi= η(ti,w1)…η(ti,wn)∈Rn, i=1,…,N (1) One looks for a set of orthonormal basis vectors uj∈Rn, j=1,2,…,n , such that ηi=j=1nγjiuj , with i=1, 2,…,N , that is, η1…ηN=u1…unγ11…γ1N⋮⋱⋮γn1…γnN, U*U=In (2) where In∈Rn x n is the identity matrix, Η=η1…ηN, U=u1…un and * is the (conjugate) transpose operator.
The uj are referred to as empirical eigenfunctions or principal direction of the “cloud” of data ηi.
As a second step, a reduction of n is also investigated.
Up to now local linearizations were adopted to support the model order reduction.
Model Order Reduction: Theory, Research Aspects and Applications, Springer, 2008

In order to get better PAPR reduction performance, we propose a new PAPR reduction algorithm based on parametric minimum cross entropy(PMCE).
PAPR Reduction Using Hexagonal Constellation And Parametric Minimum Cross Entropy (PMCE) Algorithm Let us denote the data block of length as a vector , where is the number of subcarriers.
For each data block, denote the number and index set of subcarriers where constellation points have two representations in hexagonal constellations as and respectively, where .
Comparison of PAPR reduction by different methods.
In order to get better PAPR reduction performance, we propose a new PAPR reduction algorithm based on parametric minimum cross entropy (PMCE).

The ion induced-reduction eliminates the need for high temperatures typically required for the reduction processes.
The XPS spectra of the as-grown sample is characterized by a doublet with the W 4f7/2 component at a binding energy (BE) of 35.6 eV and an energy separation between the W 4f7/2 and W 4f5/2 peaks of 2.2 eV, which agrees well with the data for pure WO3 (W6+ ionic state of tungsten) from the literature [31], [36], [37].
Closed circles represent experimental data and solid lines the fitting doublets of mixed G-L functions.
These results align qualitatively with previous data obtained from WO₃ samples bombarded with Ar+ ions [36], [37].
Closed circles represent experimental data and solid lines the product of mixed G-L functions.

In order to explore methods of improving phosphorous and nitrogen removal in sludge reduction technologies, an advanced process combining sludge reduction and phosphorous and nitrogen removal was developed, for short, HA-A/A-MCO Process (Hydrolysis-Acidogenosis -Anaerobic/Anoxic-Multistep Continuous Oxic tank).
Introduction An advanced process combining excess sludge reduction and phosphorous and nitrogen removal is developed,for short, HA-A/A-MCO process (Hydrolysis-Acidification-Anaerobic/ Anoxic-Multistep Continuous Oxic tank), which is helpful for improving phosphorous and nitrogen removal in sludge reduction technologies[1-3].
HA-A/A-MCO process has better performance of simultaneous sludge reduction and phosphorous and nitrogen removal.
HA-A/A-MCO is an advanced sludge reduction process which is developed by our research group, whose flow path is shown in Fig.1. 1.
Raw water Raw water hydrolysis Raw water +2% naerobic phosphorus release sludge hydrolysis 21% 39% 16% 24% 25% 40% 25% 10% 14% 21% 41% 24% Fig. 3 Changes of COD components from Fig. 4 Variation of VFA of each tank effluent of hydrolysis-acidification tank The data in figure shows that in test raw water soluble COD of total COD ( mean 361.5mg/L ) is 40% ( 144.6mg/L ), where VFA accounts for 16% of the total COD, about 58mg/L; Settleable COD and ( ultra ) colloidal COD accounts for 60% of the total COD ( 217mg/L ).

Rough set only deals with discrete data, but the original attribute value is consecutive, so the data must be discredited.
The way of equivalent space interval is used and reduct attribute is taken out, and then obtain discrete data outcome listed in TABLEⅡ.
Discrete data outcome U a f D 1 1 1 1 2 1 1 1 3 4 2 2 4 4 3 2 5 4 4 3 6 4 4 3 7 2 2 4 8 2 3 4 9 1 1 1 10 4 2 2 11 4 4 3 12 2 2 4 The last decision TABLEⅢ. comes from TABLEⅡ. through condition attribute reduction.
Conclusions The condition attribute reduction algorithm proposed in this paper has universal property, so it can be used in other information domain, and it is more effective for the higher dimensional condition attribute and data.
[8] Parpinelli R S, Lopes H S, Freitas, “Data mining with an ant colony optimization algorithm,” IEEE Transactions on Evolutionary Computation, vol. 6(4), 2002, pp.321-332

The intellectual primary equipments are configured with a lot of sensors, so they can convert signals from analog form to digital form, and transmit data to the automation operating system of the power grid with optical fiber ethernet in the substation.
The Rough Set Theory The Rough sets theory is a mathematical formalism to deal with incomplete data, uncertainty in knowledge discovery [1].
It can not only efficiently analyze and process the imprecise, inconsistent, half-baked information, but also can discover hidden knowledge and reveal the potential laws through data reasoning.
The main advantage of rough set theory in data analysis is that it does not need any preliminary or additional information about data comparing with probability analysis method in statistics.
Value Reduction of Decision Table The decision table after the attribute reduction should do the value reduction.

The Method Research on Data Mining of Concept Lattice Liu Chun1, a, WangDong Xing2,b , Tan Kun3,c 1, 2, 3Department of computer science and information technology, Daqing Normal University, Daqing City, Heilongjiang Province, China a asaralc@126.com, b bcnwindy02@163.com, c cdq_tankun@126.com Keywords:Data mining, Concept lattice, Algorithm, Attribute reduction Abstract.Concept lattice in essence describe the links between objects and attributes,demonstratesthe generalization and specialization of concepts.
The corresponding Hasse diagrams realize the visualization of the data.
The last part focuses on the application of concept in data mining.
The concept of data mining Generally speaking, data mining isthe process that extracts potential useful information and knowledge which hidden, not known in advance.They are similarto terminology, such as discovery knowledge from databases, data integration, data analysis, data fusion and decision support, etc.
Raw data can be structured, as data in a relational database can also be semi-structured, such as text, graphics, images, data, or heterogeneous data distributed across network.The methods find knowledge can be mathematics or non-mathematics; interpreted or summed.

The test proved the drag reduction effect of soft dolphin skin.
Each test data is average values after test three times. 3.1 NACA4412 Airfoil The drag reduction rate, lift increase rate and lift-drag ratio change rate of airfoil are calculated by the following formulae: （1） （2） （3） Fig.8 is the relation of inflow velocity and drag for NACA4412 airfoil, and Fig.9 is the relation of inflow velocity and drag reduction rate for NACA4412 airfoil with bionic soft surface.
Turbulent drag reduction using soft surface[J].
Test Research on Drag Reduction of Soft Wall [J].
Test on Drag Reduction of Soft Surface and Research of Drag Reduction Mechanism.

Synthesis of boride composite powder via fused and carbon thermal reduction Dongdong Meng1, a, Chengliang Ma1, b, Yong wei Li1, c 1Zhengzhou University, Zhengzhou, 450052, China a690895262@qq.com b13623816850@139.com c805358250@qq.com Key words: Fused method, carbon thermal reduction, high-performance boride composite powder Abstract.
To properly cope with the problems and meet the demand of high performance, applying the fused and carbon thermal reduction method as well as combining with the advantages of EAF are necessary not only to produce high performance and low cost boride compound but also to succeed in the industrial production and application for this material.
To synthesize the high-performance boride compound and confirm the best choice of boron source, carbon source and agent, adjusting the category and addition of carbon source, boron source and the agent during the synthesis process, according to the analyzed data from XRD, is essential.
The main reason accounting for this phenomenon is attributed to constant adjustment of the category and addition amount of carbon source, boron source to complement the loss of boron source as well as the agent for crystal type conversion during the synthesis process according to the analyzed data of XRD.
Conclusions 1) The fused and carbon thermal reduction method is feasible to synthesize the boride composite powder.

Results and Discussion The X-ray diffraction data of the SBN61 samples are shown in Figure 1.
The oxygen-reduction degree increases in the order of SBN61Ar, SBN61H1100, and SBN61H1250.
According to the X-ray diffraction data, the lattice parameters and the theoretical densities of the samples were calculated, as shown in Table 1.
It indicates that oxygen-reduction can increase the κl of the SBN61 ceramics.
However, when the oxygen-reduction achieves some degree, the deepening of the oxygen-reduction degree has little effects on the increase of the κl.